The Optimality Conditions Of Vector Optimization And Descending Algorithm For Some Types Of Nonlinear Programming Problems

In this thesis, some topics on the infinite dimensional vector extremum problems and some algorithms for the nonlinear programming problems are discussed. Using the alternative theorem, the optimality conditions of vector extremum problems with generalized constraint are established in ordered linear space. In the ordered linear topological space, the concept of the gradient of G-differentiable function is introduced. Applying the theorem of alternative of subconvexlike map and other some conclusions, the optimality conditions represented by gradient for the vector extremum problems with generalized constraint are obtained. And we discuss the efficiency of the vector extremum problems. Then, we gained some algorithms of the nonlinear programming problems.Firstly, we added the inaccurate one dimension researching method to the original descending algorithm in the nonlinear programming problem with the linear equality constrains and established a new method. Secondly, we reseach the new algorithm in the indefinite quadratic programming. Morever, we proved that the algorithms we gained are efficent and correct by using a lot of examples.